an investigation of dual stator winding induction machines

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ei where, exp( − jϕ ) = cos( ϕ ) − jsin( ϕ ) , cos( ϕ ) and sin( ) i i i i 304 ω = ω + a Then the rotor flux linkages are estimated using stator flux linkages as: λ λ qri dri where, L = L ri mi L = L L σ i ri mi ⋅ ⋅ = L ( λ − L I ) qsi ( λ − L I ) si dsi L − L 2 mi ri σ i σ i . qsi dsi 8.7 Simulation and Experimental Results 2 ei 2 i = ω a i ϕ i . 2 2 ei + ai (8.52) The models of the generator systems are built up using the MATLAB/SIMULINK to evaluate the proposed control scheme for the parallel rectifier. The parameters of the dual winding induction machine are given in Table 8.2. The simulation results in Figure 8.5 show the starting process of the machine. The rotor speed is maintained at 188 rad/s. The reference dc voltage is set to be 240V. It is clearly shown that by using the proposed control scheme, the dc voltage is well regulated. The dynamic responses of the generation system to changes in load and portioning coefficient K are shown in Figure 8.6. When the rotor speed is constant and the system is running at the steady state, the load resistance is changed from 90 Ω to 60 Ω at 1.5 s, rotor speed changes to 168 rad/s from 2.2 s to 2.5 s, while the power distribution coefficient K is changed from 1 to 3 at 2.8 s to see how it influences the output power of each winding. The dc voltage adequately tracks the reference under the dynamic situation.
Table 8.2 Machine parameters for simulation and experimental implementation ABC winding XYZ winding Number of pole 2 6 Stator resistance r = 3. 4 Ω r = 1. 9 Ω s1 Mutual inductance = 0. 336 H 0. 093 H Lm1 305 s2 Lm2 = Leakage inductance = 0. 006 H 6 0. 009 H Lls1 Lls2 = Rotor resistance r = 0. 61 Ω r = 0. 55 Ω r1 Significant redistribution of required power from each stator winding is manifested in the value of the electromagnetic torque of each winding. For changes in load, power distribution coefficient and rotor speed, the controlled dc voltage effectively tracks the command. The proposed input-output linearization method for controller design results in a decoupled q-d control scheme, however the calculations of the excitation input command voltages are dependent on the knowledge of the machine parameters, in which the magnetizing inductances, the stator and rotor resistances are parameters that vary under different operating conditions. The dynamic responses of the proposed control system to the changing parameters are simulated to check the robustness of the control scheme and the simulation results are shown in Figure 8.7. The magnetizing inductances of both stator winding sets are increased by 10% of their rated values while the rotor resistances increase by 50% of their rated values as shown in Figure 8.7 (h-k). When the parameters change, the dc voltage is well regulated to be constant. It is found from the simulation results that the change of the rotor resistance of the XYZ winding set has relatively r 2
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AN ABSTRACT OF A DISSERTAION AN INV
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coupling and interaction terms are
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CERTIFICATE OF APPROVAL OF DISSERTA
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ACKNOWLEDGEMENTS I would like to ex
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vi Page 2.2 Machine Design I.......
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viii Page 4.2.3 Self Inductances of
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x Page 7.3.4 f = 30 Hz and f = 95 H
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xii Page 10.8 D-decomposition Metho
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LIST OF FIGURES xiv Page Figure 1.1
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Figure 3.10 The simulation of the s
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Figure 3.34 Measured flux densities
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xx Page Figure 4.8 Self-inductance
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Figure 5.2. Simulation results for
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Figure 6.8. The dynamic response of
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Figure 7.22. Copper losses of the m
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Figure 8.7. The dynamic response of
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Figure 9.4 Steady state analysis, (
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Figure 9.12. The steady state wavef
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xxxiv Page Figure 10.16 Pole-zero m
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Figure 11.2 Per phase equivalent ci
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CHAPTER 1 INTRODUCTION AND LITERATU
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The last is the recently developed
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It should be noted that at any time
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A. R. Munoz and T.A. Lipo are pione
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has to be modified to adapt to thes
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circuit model of an induction machi
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ωr stator rotor 13 ωr rotor (a) (
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1.2.4 Field Analysis Method In [5.1
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separated dc source, etc. From the
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in [8.14]. In [8.15-8.17], the stud
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[8.22] and the total losses of the
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proposed. The switching frequency i
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The actual rotor mechanical speed i
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1.2.9 Induction Machine Drive---Vec
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stator windings were used as flux s
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The rotor flux can be obtained by:
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The basic idea of a closed loop flu
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estimation. It has been claimed in
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{ k [ ˆ* ( i iˆ ) ] ( k) [ ˆ* Im
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integral and a new stretch-turn ope
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The most recent overview paper is g
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CHAPTER 2 DUAL STATOR WINDING INDUC
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Table 2.1 Parameters of machine des
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A C B 2.2.2 Air Gap Flux Density X
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where, ω s1 and s2 respectively.
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There are two unknown variables in
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Since small machines typically have
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N s E = (2.18) 4. 44 fK φ 1 m Flux
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conduct away the heat produced in t
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k cs τ s = 2 2b ⎪ ⎧ ⎡ ⎤⎪
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are: Fts = H ts( ave) d s ( ave) =
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1 2 1 = H o ( ) + H o ( ) + H cr 90
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The skew of the stator winding is n
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0 bs Figure 2.5. Detailed stator sl
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y: The pole pitch at the mid point
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L lsk = L m ( α 2) ⎪⎧ ⎡sin
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2.3.4 Rotor Bar Resistance r b The
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2.3.7 Rotor Resistance Referred to
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Substituting δ = π into (2.97) an
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atio also increases. The air gap fl
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From (2.105-2.108), the ratio of th
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2.5 Conclusions In this chapter, a
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A recently developed dual stator wi
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stator winding induction machine ba
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∫ H ⋅ dl = ∫ J ⋅ ds = N ⋅
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theory itself is correct. The inacc
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( θ ) ⋅ g( θ, θ ) − H ( 0)
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where ( θ ) n A is the average of
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Since the definition of the mutual
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3Cs1 Cs1 − Cs1 − 3Cs1 6Cs1 4Cs1
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3.4.2 Mutual Inductances of the ABC
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where, ( θ ) n is the average of t
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1 0 α 1 − r 2π α − r 2π Fig
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When the skewing factor of the roto
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3.6 Calculation of Stator-Rotor Mut
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dλ v = R ⋅ i + (3.58) dt where,
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3.7.1.3 Stator flux linkage in ABC
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where, r R is the resistance matrix
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Only terms in equation (3.77) which
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119 ( ) ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
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−1 −1 −1 where, λ qdr = Tr L
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3.16 and Figure 3.17. It is found f
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Figure 3.11 The simulation of the d
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Figure 3.14 The simulation of the s
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Figure 3.16 Rotor bar currents duri
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Phase Y Figure 3.20 Air gap flux de
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Figure 3.24 Total air gap flux dens
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Figure 3.27 The air gap flux densit
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Figure 3.29 Air gap flux density co
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Figure 3.33 Air gap flux density in
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All the waveforms shown above are t
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Figure 3.39 Air gap flux density pr
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Figure 3.42 Normalized spectrum of
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CHAPTER 4 FULL MODEL SIMULATION OF
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Substituting (3.28) and (3.29) into
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Figure 4.3 Self-inductance under 20
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Figure 4.4 Mutual inductance under
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that L AB = L BA , L BC = L CB and
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the assumption that the rotor skew
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4.4 Mutual Inductances Calculation
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Figure 4.24 Stator rotor mutual ind
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Figure 4.25 Stator rotor mutual ind
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varying inductances excited by four
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Equations similar to (4.15-4.16) we
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the number of poles for the winding
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Figure 4.29 Dynamic response of dua
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(a) (b) (c) (d) Figure 4.32. Normal
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CHAPTER 5 FIELD ANALYSIS OF DUAL ST
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In the analysis that follows the fu
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where, C s1 is the number of series
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θ , ∂B1 µ 0r = ⋅ J1 θ ∂θ
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C C = k π ⋅ d s2 s2 s2 199 (5.19
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the XYZ winding set is obtained by
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u rpi 2π ' k − jk θ −( i−1)
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The corresponding flux densities in
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The first term in equation (5.55) i
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The second term in (5.64) is zero u
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5.2.2 Torque Equation The calculati
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Re j( ω ) ⎧ 1t− P1θ µ 0r j(
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* ( ) ( ) ( ) ⎛ P1 ⋅ ⋅ ⎞ j
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* Since both ( ) C 2π ∫ 0 2 * Cs
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(A) Induced voltage in the ABC wind
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5.3.3 Equation of Torque Contribute
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winding set works as a generator, w
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possible for the brushless doubly-f
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Since the number of rotor bar is n,
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5.6 Computer Simulation and Experim
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Figure 5.2. Simulation results for
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5.7. Conclusions In this chapter, u
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good steady-state predictions and c
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which are superimposed some space h
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(a) (b) (c) Figure 6.1: Main flux s
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(a) (b) (c) (d) (e) Figure 6.3: Fin
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(a) (b) Figure 6.5: Induced air-gap
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Substituting (6.7) into (6.4-6.6),
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L L L L L L L λ + lr1 m1 ls1 m1 lr
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6.4 Simulation and Experimental Res
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Figure 6.7 . Simulation results for
Page 293 and 294: Figure 6.9 Experimental results for
Page 295 and 296: diminish the contribution of the 6-
Page 297 and 298: CHAPTER 7 STEADY STATE ANALYSIS OF
Page 299 and 300: where, L L = (7.11) si mi iqdri λq
Page 301 and 302: Overall efficiency of the dual stat
Page 303 and 304: Figure 7.2 Stator current speed cha
Page 305 and 306: Figure 7.6 Power factor speed chara
Page 307 and 308: Figure 7.9 Power factor speed chara
Page 309 and 310: 7.3.5 f = 35Hz and f = 90 Hz abc xy
Page 311 and 312: Figure 7.16 Torque speed characteri
Page 313 and 314: this conclusion is based on the ass
Page 315 and 316: Figure 7.21. ω s1 vs s2 ω when to
Page 317 and 318: Figure 7.25 ω s1 vs s2 ω when the
Page 319 and 320: Figure 7.28. Copper losses of the m
Page 321 and 322: 7.4 Conclusions Based on the steady
Page 323 and 324: applications and possible use as st
Page 325 and 326: L pλ + λ = I − = σ (8.3) ( ω
Page 327 and 328: espectively. The stator q and d axi
Page 329 and 330: * 3 * ( V I ) V Re( M I ) 3 P p = R
Page 331 and 332: the modulation index of the rectifi
Page 333 and 334: Lie derivative and relative order d
Page 335 and 336: The above algorithm requires that t
Page 337 and 338: σ = 3 1+ K ( Vqs1iqs1 + Vds1 ds1)
Page 339 and 340: Butterworth polynomial with the den
Page 341 and 342: Table 8.1 Parameters of controllers
Page 343: generally the case to get a good pe
Page 347 and 348: (a) (b) (c) (d) (e) (f) (g) Figure
Page 349 and 350: (a) (b) (c) (d) (e) (f) (g) (h) (i)
Page 351 and 352: (a) (b) (c) (d) (e) (f) (g) (h) (i)
Page 353 and 354: CHAPTER 9 HIGH PERFORMANCE CONTROL
Page 355 and 356: The qd0 voltage equations of a dual
Page 357 and 358: 317 ( ) ( ) ( ) ( ) ( ) ⎥ ⎥ ⎥
Page 359 and 360: If the rotor speed and the rotor fl
Page 361 and 362: Infeasible region (a) Vdc1 and Vdc2
Page 363 and 364: The influences of the saturation of
Page 365 and 366: Figure 9.5(a), by varying the q-axi
Page 367 and 368: Figure 9.5 Steady state analysis, (
Page 369 and 370: L1 L3 2 ( 1− K ) Vdc1 3 = ( Vqs1i
Page 371 and 372: If the PI controllers are used and
Page 373 and 374: egulation capabilities of the contr
Page 375 and 376: (a) (b) (c) (d) (e) (f) (g) (h) (k)
Page 377 and 378: (a) (b) Figure 9.11. The starting p
Page 379 and 380: 9.6 Conclusions The high performanc
Page 381 and 382: induction machine are applicable to
Page 383 and 384: In section 10.2, the fundamentals o
Page 385 and 386: The vector control of an induction
Page 387 and 388: possibilities for fault conditions,
Page 389 and 390: where, where, − r r L = (10.18) (
Page 391 and 392: qsi qsi * ( I I ) σ = K ⋅ − (1
Page 393 and 394: In the proposed control scheme, rot
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* ωr * ωr + + − ωr k p + ki s
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The value of ω 0 determines the dy
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10.4.4 Stator D-axis Current Contro
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(a) (b) (c) (d) (e) (f) Figure 10.4
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The proposed control scheme has als
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(a) (b) (c) (d) (e) (f) (g) Figure
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10.6 Full-order Flux Observer The c
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while the second three-phase windin
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L r L p ˆ λ ˆ ˆ (10.66) ri si r
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373 [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( )
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t 2bi ⎛ rsiLri K iL ⎞ ⎛ ri K
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ri D i si ri ri si mi ri 2 ( K )
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esults show that the selected obser
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Figure 10.12 The poles of the 6-pol
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383 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
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⎧t s ⎨ ⎩ts 1 2 = t = t 1 2 Th
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Figure 10.15 The poles of the machi
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X i i = X Y = Y i i ( σ , ω) ( σ
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this error is used as the feedback.
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ˆ ω rm The output error is expres
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The expressions of t1 i and t2 i ar
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397 ( ) ( ) ( ) bi ei i bi ei i ai
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The transfer function of rotor spee
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(a) (b) (c) (d) Figure 10.16 Pole-z
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Figure 10.19 Pole-zero maps with di
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Figure 10.22 Pole-zero maps with di
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should ensure the stability under a
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The boundary of the speed controlle
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10.11 Simulation Results for Sensor
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Figure 10.28 Speed estimation for 2
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(a) (b) Figure 10.31 Speed estimati
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(a) (b) (c) (d) (e) (f) Figure 10.3
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Figure 10.34 Actual and estimated v
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CHAPTER 11 HARDWARE IMPLEMENTATION
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esistance for two phase windings. T
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11.2.3 Short Circuit Test The short
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When the input voltages of 2-pole A
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winding set is generating and the o
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11.4 Per Unit Model For the fixed p
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1 = 12 2 0. 0024414 The transformat
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ase values of voltage/current. The
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Start System configuration Initiali
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CHAPTER 12 CONCLUSIONS AND FUTURE W
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Using the rotating-field theory and
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each winding have been clearly show
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voltages of different frequencies,
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REFERENCES 447
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[2.2]. P. C. Roberts, "A Study of B
Page 491 and 492:
[5.3]. R. A. McMahon, P. C. Roberts
Page 493 and 494:
[8.17]. O. Ojo, “Performance of s
Page 495 and 496:
[10.5]. J. C. Moreira, K. T. Hung,
Page 497 and 498:
[10.27]. M. Hinkkanen, “Analysis
Page 499 and 500:
[10.48]. K. Lee and F. Blaabjerg,
Page 501 and 502:
VITA Zhiqiao Wu was born in Shashi,
Page 503:
3. Zhiqiao Wu and O. Ojo, "High Per
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